The double-diffusivity heat transfer model for grain stores incorporating microwave heating

Abstract

Australia’s reputation is well established in the international marketplace as a producer of high-quality grain. One of the largest problems faced by the Australian grain industry is protecting grain, while in storage, from infestation by insect pests. The standard practice employed is to fumigate with chemicals such as phosphine. Currently, there is an ongoing reduction in the number of chemicals permitted for pest control, as insects have developed resistance to some chemicals and others are currently being phased out due to safety and environmental reasons. As a result, the grain storage industry is moving towards physical methods as opposed to chemical methods, as a safer and potentially better alternative. One well studied area is known as thermal disinfestation, with one of the potentially best forms being heat disinfestation via microwave radiation. The mathematical modelling of microwave heating processes in general requires the solution of a complex system of equations, which can be very difficult to obtain. In this work we illustrate the possibility of reducing the problem to one which involves extending the double-diffusivity heat transfer model, as previously developed by the authors [Aust. NZ Ind. Appl. Math. J. 42 (E) (2000) C117], to include a non-linear body heating source term to account for the heating due to microwave radiation. This model is known as the double-diffusivity heat transfer model incorporating microwave heating. Such a dual-region model is well suited to the analysis of grain bulks as air and grain are two different mediums with different heat conduction properties. A semi-analytical solution is obtained via the heat-balance integral method and is compared with an explicit finite difference numerical solution. Very good agreement is found between both forms of the solutions. We also compare these results to the case of no microwave heating, that is, the double-diffusivity heat transfer model [Aust. NZ Ind. Appl. Math. J. 42 (E) (2000) C117].